This invention relates to digital communications systems. More particularly, the invention relates to communications systems in which the characteristics of digital signals transmitted via radio waves are modified to achieve spectral efficiency and high bit rate. Systems with high bit rates are generally desirable to maximize the amount of information which is transmitted per unit time. Systems with high spectral efficiency are also desirable to maximize the number of users which can effectively occupy a given portion of frequency spectrum. Those skilled in the digital radio communications art appreciate that the goal of achieving a high bit rate in digital radio communications systems is generally in conflict with the goal of frequency spectrum conservation. That is, if the bit rate of the transmitted digital signal is increased, the amount of frequency spectrum consumed tends to increase as well.
Other factors which affect spectral efficiency include the power of the transmitted digital radio signal. That is, if a particular type of digital modulation requires a relatively high amount of power in order to permit proper detection at the receiver, then such high power transmission is more likely to cause interference to signals on adjacent channels than digital modulation techniques which require lower power to achieve the same amount of receiver sensitivity or effective reception.
A key issue in designing an efficient digital transmission system is the selection of the prototype pulse which is used to represent a transmitted symbol. Those skilled in the digital communications art also refer to such a prototype pulse as the "signalling waveform". The possible signalling waveforms to be transmitted are given by the mathematical expression k.sub.n *p(t), wherein p(t) is the prototype pulse and k.sub.n is one member of a set of constants. For example, a binary transmission system frequently uses k.sub.o =-1 to transmit a "0", and k.sub.1 =1 to transmit a "1".
For best power efficiency, the prototype pulse must have low intersymbol interference. In mathematical terms, the set of signalling waveforms must be an orthogonal set, or a nearly orthogonal set.
For best spectrum efficiency in transmission, the prototype pulse must have the most compact possible spectrum.
For best efficiency in the hardware used for encoding and decoding transmitted signals, the prototype pulse must be as short in time as possible. The complexity of the hardware tends to be proportional to the length of the prototype pulse or signalling waveform.
The three efficiency criteria expressed above tend to be mutually exclusive. That is, optimizing one of the criteria tends to make at least one of the other criteria unsatisfactory. For example, a rectangular prototype pulse with a length of one bit time is optimized for minimized pulse length. Unfortunately, the broad spectrum of such prototype pulse is hundreds of times wider than what is required to transmit information. A substantially opposite example is the case where the prototype pulse is a sin(pi*t)/(pi*t) pulse. Such a pulse has the most compact frequency spectrum possible, but unfortunately its pulse length in the time domain is hundreds of times that of the rectangular prototype pulse.
It is believed that no prior method or apparatus has successfully generated a prototype pulse or signalling waveform which fully satisfies all three of the above efficiency criteria simultaneously.